Updating quasi newton matrices with limited storage

It is shown that the matrices generated have some desirable properties.

The test problem collections for nonconvex unconstrained minimization are taken from Moré et al. For middle-scale problems, the accuracy of NTR is higher, but the cpu time of NLMTR is shorter.Then the corresponding trust region method is proposed for large-scale unconstrained nonconvex minimization.The global convergence of the new algorithm is proved under some appropriate conditions. In the next section, we deduce a new straightforward limited memory quasi-Newton updating.We derive compact representations of BFGS and symmetric rank-one matrices for optimization.These representations allow us to efficiently implement limited memory methods for large constrained optimization problems.

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